Injecting Abstract Interpretations into Linear Cost Models

We present a semantics based framework for analysing the quantitative behaviour of programs with regard to resource usage. We start from an operational semantics equipped with costs. The dioid structure of the set of costs allows for defining the quantitative semantics as a linear operator. We then present an abstraction technique inspired from abstract interpretation in order to effectively compute global cost information from the program. Abstraction has to take two distinct notions of order into account: the order on costs and the order on states. We show that our abstraction technique provides a correct approximation of the concrete cost computations

Private Valuation of a Public Good in Three Auction Mechanisms.

We evaluate the impact of three auction mechanisms – the Becker–DeGroot–Marschak (BDM) mechanism, the second-price auction (SPA), and the random nth-price auction (NPA) – in the measurement of private willingness-to-pay and willingness-to-accept for a pure public good. Our results show that the endowment effect is lower with the BDM mechanism. In this market mechanism, the effect disappears after a few repetitions. Yet, on a logarithmic scale, the random nth-price auction yields the highest speed of convergence towards equality of welfare indices. We also observe that subjects value public goods in reference to their private subjective benefit derived from their public good funding.auction mechanisms; WTP-WTA disparity; private provisions; public goods;

Global integration of the Schr\"odinger equation within the wave operator formalism: The role of the effective Hamiltonian in multidimensional active spaces

A global solution of the Schr\"odinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A: Math. Theor. 48, 225205 (2015)], is generalized to take into account the case of multidimensional active spaces. An iterative algorithm is derived to obtain the Fourier series of the evolution operator issuing from a given multidimensional active subspace and then the effective Hamiltonian corresponding to the model space is computed and analysed as a measure of the cyclic character of the dynamics. Studies of the laser controlled dynamics of diatomic models clearly show that a multidimensional active space is required if the wavefunction escapes too far from the initial subspace. A suitable choice of the multidimensional active space, including the initial and target states, increases the cyclic character and avoids divergences occuring when one-dimensional active spaces are used. The method is also proven to be efficient in describing dissipative processes such as photodissociation.Comment: 33 pages, 11 figure

The development and testing of an emotion-enabled, structured decision-making procedure

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Two contrasting forms of advice for decision-makers are to either follow one’s heart (emotions) or one’s head (reason). This is a false dichotomy – but how should decision-makers combine heart and head? Decisions can be fruitfully analysed as a set of components: a decision-problem embedded within an on-going situation, with values-at-stake, possible options-with-consequences, choice, action and review. Structured decision-making models (head theories) approach this multifaceted nature of decisions by a divide-and-conquer strategy with thinking tasks provided to help decision-makers clarify the decision-problem, identify important values-at-stake, find credible options, choose the most credible option, act effectively and fairly review the outcomes of the choice. Emotions are complex and can also fruitfully be analysed as a set of components: an appraisal of a situation’s implication for the actor’s goals and values, bodily and cognitive changes, phenomenological experience and desires. Emotions can both help and hinder decision making, so wise decision-makers should neither ignore nor rely upon emotions, but instead treat emotions as fallible resources. The complex nature of emotions implies that different emotion-enabled tasks might assist decision-makers for different components of the decision. On the basis of this analysis an emotion-enabled, structured, decision-making procedure was developed and investigated by taking ten participants with decision dilemmas through the procedure. This investigation, based on repeated use of the Hermeneutic Single-Case Efficacy Design, provided some initial support for the effectiveness of the model: participants found the procedure generally helpful (p < 0.005), had increased confidence in their final choice (p < 0.005), which at follow-up they were satisfied with (p < 0.005). The use of emotions as fallible resources was also investigated through tracing emotion-enabled changes in participants’ decision making. Suggestions for further development and investigation of integrating emotions into structured approaches are offered

Constrained Adiabatic Trajectory Method (CATM): a global integrator for explicitly time-dependent Hamiltonians

The Constrained Adiabatic Trajectory Method (CATM) is reexamined as an integrator for the Schr\"odinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent or explicitly time-dependent Hamiltonians. The emphasis is put on adiabatic processes and within this adiabatic framework the interdependence between the CATM, the wave operator, the Floquet and the (t,t') theories is presented in detail. Two points are then more particularly analysed and illustrated by a numerical calculation describing the $H_2^+$ ion submitted to a laser pulse. The first point is the ability of the CATM to dilate the Hamiltonian spectrum and thus to make the perturbative treatment of the equations defining the wave function possible, possibly by using a Krylov subspace approach as a complement. The second point is the ability of the CATM to handle extremely complex time-dependencies, such as those which appear when interaction representations are used to integrate the system.Comment: 15 pages, 14 figure

Controlling vibrational cooling with Zero-Width Resonances: An adiabatic Floquet approach

In molecular photodissociation, some specific combinations of laser parameters (wavelength and intensity) lead to unexpected Zero-Width Resonances (ZWR), with in principle infinite lifetimes. Their interest in inducing basic quenching mechanisms have recently been devised in the laser control of vibrational cooling through filtration strategies [O. Atabek et al., Phys. Rev. A87, 031403(R) (2013)]. A full quantum adiabatic control theory based on the adiabatic Floquet Hamiltonian is developed to show how a laser pulse could be envelop-shaped and frequency-chirped so as to protect a given initial vibrational state against dissociation, taking advantage from its continuous transport on the corresponding ZWR, all along the pulse duration. As compared with previous control scenarios actually suffering from non-adiabatic contamination, drastically different and much more efficient filtration goals are achieved. A semiclassical analysis helps in finding and interpreting a complete map of ZWRs in the laser parameter plane. In addition, the choice of a given ZWR path, among the complete series identified by the semiclassical approach, amounts to be crucial for the cooling scheme, targeting a single vibrational state population left at the end of the pulse, while all others have almost completely decayed. The illustrative example, offering the potentiality to be transposed to other diatomics, is Na2 prepared by photoassociation in vibrationally hot but translationally and rotationally cold states.Comment: 15 pages, 14 figure

Mid-infrared resonant ablation of PMMA

Laser ablation proved to be a reliable micro-fabrication technique for patterning and structuring of both thin film and bulk polymer materials. In most of the industrial applications ultra-violet (UV) laser sources are employed, however they have limitations such as maintenance costs and practical issues. As an alternative and promising approach, mid-infrared resonant laser ablation (RIA) has been introduced, in which the laser wavelength is tuned to one of the molecular vibrational transi-tions of the polymer to be ablated. Consequently, the technique is selective in respect of processing a diversity of polymers which usually have different infrared absorption bands. In this paper, we present mid-infrared resonant ablation of PolyMethyl MethAcrylate (PMMA), employing nanosec-ond laser pulses tunable between 3 and 4 microns. This RIA nanosecond laser set-up is based on a commercial laser at 1064 nm pumping a singly resonant Optical Parametric Oscillator (OPO) built around a Periodically-Poled Lithium Niobate (PPLN) crystal with several Quasi-Phase Matching (QPM) periods. RIA has been successfully demonstrated for structuring bulk PMMA, and selective patterning of PMMA thin films on a glass substrate has been implemented